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Question

Find the general term and the sum of n terms of the series 3,1,11,39,89,167,....

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Solution

31113989167....
212285078....
10162228....
666....
Assuming un=A+Bn+Cn2+Dn3
Putting n=1,2,3,4, we get;-
un=n3(n+1)2
=n3n(n2+n+1)
=(n1)n(n+1)n(n+1)1
Sn=un
Sn=14(n1)(n)(n+1)(n+2)13n(n+1)(n+2)n

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